The present invention relates generally to the measurement of color, and more particularly to the correction of spectral measurements, such as are obtained by a spectrophotometer for measuring color.
Accurate and reliable measurement of color is difficult to achieve, but is essential for successful color reproduction and control. xe2x80x9cColorxe2x80x9d is the human visual system""s response to a specific distribution of light energy in what is termed the xe2x80x9cvisible spectrumxe2x80x9d, a portion of the full electromagnetic energy spectrum where the wavelength ranges from 400 nanometers (1 nm =10xe2x88x929 meters) to 700 nm. A plot of light energy versus wavelength is called a spectrum. As an example, a spectrum for the color Magenta is shown in FIG. 1. The various possible shapes of the spectrum plot gives rise to the perception of different colors. For example, spectra which have larger energy amplitudes in the short wavelengths near 400 nm are perceived as being xe2x80x9cbluexe2x80x9d while spectral plots that show larger amplitudes in the longer wavelengths near 700 nm are perceived as being xe2x80x9credxe2x80x9d. The set of all possible shapes for a spectral energy plot gives rise to the enormous number of colors that humans can see (nearly 10 million). In the case of visible light, each spectral band of color may be as small as 2 nm wide spanning the range from 400 nm to 700 nm.
A wide variety of instruments are used to make quantitative measurements of color. In general, these instruments can be classified as making either xe2x80x9cthree-bandxe2x80x9d, or xe2x80x9cfull spectrumxe2x80x9d measurements. The three-band instruments measure the light energy reflected from a sample at three positions within the spectrum. They are not able to detect the entire spectrum of a color, but having a 3-channel estimate of it is very useful for many printing and color control applications, and the expense of making this kind of measurement is low.
Full spectrum instruments are able to obtain the spectral energy distribution of a color across the entire visible spectrum, and thereby gain a more accurate representation of the color characteristics of a sample. For example, such a measurement can be used to predict a sample""s color appearance even when the lighting on the sample changes.
The more accurately a spectrum is measured, the better will be the color representation, and so very high resolution spectra (many sampling positions along the wavelength axis) are desirable. It is difficult however, to make accurate and high resolution full spectrum measurements.
For a variety of reasons related to the specific design of an instrument, the amplitude at one position (one wavelength) along the spectrum is influenced by the amplitudes at other wavelengths. This is called xe2x80x9ccross-spectrum contaminationxe2x80x9d or xe2x80x9ccrosstalkxe2x80x9d. If the amplitude measured at some position in the spectrum is distorted by crosstalk, the spectrum will misrepresent the color of the sample.
FIG. 2 illustrates an example of this effect. FIG. 2 shows a spectrum of a blue sample. The plot of actual spectra 10 shows that the reflected energy from the sample is highest in the short wavelength region and the spectrum makes a transition to a low level for the rest of the wavelengths. A plot of a spectrum that might be measured by an instrument suffering from spectral crosstalk is shown at 12. Plot 12 shows a rise in energy at the long wavelength end that does not really exist, it is a false measurement of the blue energy showing up as an apparent amount of red. In other words, plot 12 shows energy from the blue end of the spectrum being falsely detected as energy from the red end of the spectrum. The color represented by the measurement will have a reddish tint compared to the actual color.
If it could be determined just how much the blue wavelength energy was influencing the red wavelength measurements, we could compensate for this effect. Unfortunately, a single measurement isn""t enough to discover exactly what wavelength is causing the contamination. The contamination could be any of the wavelengths in the blue region, it could be a little contamination from all of the wavelengths, the contamination could be from just a portion of the wavelengths, or from a gradual increase of contamination toward one specific wavelength.
To find out the details of the crosstalk in order to correct for it, many measurements must be taken of unique color spectra, and then the influencing wavelengths must be factored out. The number of measurements that must be made is equal to the number of wavelength positions along the spectrum that are used in the spectral plot. It is common to have at least 30 such positions, but more accurate instruments using higher resolution obtain over 100 individual amplitudes for a spectral plot. It becomes difficult to solve for the crosstalk characteristics for such a large system.
In addition, the nature of the light source used to illuminate a color specimen can have considerable effect on the spectrum that is detected. In particular, the angle of illumination, the texture and gloss of the sample, and the amount of ultraviolet energy in the light and fluorescent material in the sample, all influence the spectrum that is obtained.
Because of these issues, prior art spectral sensing instruments incorporate many different strategies and detection techniques. Any spectral instrument design represents a collection of tradeoffs involving sensitivity, accuracy, specimen size and geometry, cost, power consumption, and the like. These tradeoffs result in considerable variation in instrument designs available on the market, and correspondingly, variations in the color measurements made by them.
It would be advantageous to provide a simple means for correcting spectral color measurements using vectors and matrices. It would be advantageous to provide for the correction of crosstalk effects as well as various other sources of spectral representation error. It would be further advantageous to provide for the correction of spectral color measurements using a single correction matrix. It would be still further advantageous to provide a correction matrix that embodies a transform that minimizes the difference between the corrected spectra and a set of reference spectra. It would be advantageous if the difference between the corrected spectra and the reference spectra could be characterized by a set of basis functions, which can be used to build the correction matrix.
The methods and apparatus of the present invention provide the aforesaid and other advantages.
The present invention provides methods and apparatus for correcting spectral measurements, such as are obtained by a spectrophotometer for measuring color. In accordance with the invention, a single matrix operates on a raw measurement vector (spectrum) to obtain a corrected spectrum. The matrix may embody a transform that minimizes the difference between the corrected spectra and a set of reference spectra. The difference may be characterized by a set of basis function weighting vectors which are then used to build the correction matrix. The method allows the correction of high resolution spectra (very long measurement vectors) without requiring the large number of measurements that would normally be required. The reference spectra can be calibration data, or measurements made by another instrument which is desired to be simulated.
This invention provides a way to solve for the crosstalk components without making hundreds of measurements for a high resolution full spectrum color instrument. Instead, a few tens of measurements can be made. The (uncalibrated) color instrument to be characterized is used to obtain spectral measurements of, for example, 24 uniquely colored sample patches. Another instrument, a reference instrument, which is known to be calibrated accurately, also makes measurements and obtains spectra of these same 24 color patches. The spectra from the reference instrument are collected and compared to the set of spectra from the uncalibrated instrument. One spectrum is subtracted from the other to obtain a spectral difference plot or error spectrum for each of the 24 colors.
It would be desirable to compare the error spectra with the original measured spectra to find how they are correlated, but as mentioned previously, it is not possible to uniquely correlate the errors with so few measurements. Such a system is said to be underdetermined, as there are many possible solutions. The number of possible solutions can be reduced, however, by making an approximation to the difference spectra. The approximation requires that each difference spectrum be represented as the sum of a number of (no more than 24 in this example) possible components. These components can be selected so that there is a minimum of residual error in this representation of the difference spectra. Well-established methods of linear algebra are used to find the components for this approximation and are described in detail below.
If the difference spectra can be represented by 24 or fewer components (the number of color patch measurements made), then a unique correlation between the measurement error and the original measured spectrum can be solved for by using standard algebraic methods (also described below). This correlation describes the relationship between the original measurement and any crosstalk error that it might contain. Since this relationship can now be calculated, the error can be computed and subtracted from the original measurement to obtain a new spectrum that no longer contains this crosstalk error.
The concept of correcting a spectral measurement is a common one. A simple correction method is to multiply the spectrum by a scale factor or to subtract an offset. Slightly more sophisticated is to scale the spectrum by a different factor at each wavelength, or to subtract a different offset from the amplitude at each wavelength. All of these operations can be accomplished using matrices, vectors, and a matrix multiply operator. A vector is used to represent the sequence of amplitudes for each wavelength along a spectrum. It is shown as a long rectangle, either horizontally oriented (a row vector), or vertically oriented (a column vector). A matrix is a collection of vectors and forms a larger rectangle. The correction matrix used in the present invention has the same number of rows as columns and may be shown as a square. These elements are combined by the matrix multiplication operation.
The multiple steps of calculating an error spectrum and then subtracting it from the measurement can be combined into a single matrix multiplication operation. The matrix that is used for this one-step procedure is the combination of a crosstalk correlation matrix with an Identity matrix resulting in a correction matrix. The identity matrix serves to represent the original spectrum. Such a technique is possible because of the properties of linear systems.
The correction matrix contains the information that correlates the crosstalk error with the spectral measurement. The actual crosstalk correction amplitudes are obtained by multiplying the spectrum by the matrix. Once the crosstalk correction is obtained, it is added to the spectrum. This is a very general and powerful technique for correcting signals and a number of useful variations are commonly used. The effectiveness of this technique depends critically on the contents of the matrix. The calculation of the correction matrix elements is described in detail below.
In an exemplary embodiment of the invention, spectral measurements of a color sensing device may be corrected. A set of spectral measurements may be obtained by the color sensing device. Each of the spectral measurements represents an amplitude of detected light in a spectral band from a plurality of respective N spectral bands, such that the set of spectral measurements may be represented by a 1xc3x97N spectral measurement vector. A set of basis function weighting vectors is calculated based on the difference between measured spectra values for a plurality of color samples and a set of reference spectra values for the same color samples. The calculation of basis function weighting vectors is described in detail below. An Nxc3x97N transform matrix is formed based on these basis weighting vectors and the measured spectra values. The Nxc3x97N transform matrix provides mapping between the spectral measurements and corrected spectra. The 1xc3x97N spectral measurement vector may be multiplied by the Nxc3x97N transform matrix to generate a corrected spectrum.
A processor may be provided for multiplying the 1xc3x97N spectral measurement vector by the Nxc3x97N transform matrix to generate the corrected spectrum.
The Nxc3x97N transform matrix may be obtained by measuring spectra values of a training set of K color samples. Each sample has a known reference reflectance spectra. Once the measured spectra are obtained, the basis function weighting vectors (a representation of the difference between the measured and the reference reflectance spectra) can be solved for using a set of D basis functions. The number of basis functions (D) may be less than or equal to the lesser of K or N. The basis functions may be represented by the D columns in an Nxc3x97D array, or in any suitable manner. The solution for the basis function weighting vectors may be represented as an array of Dxc3x97N amplitudes. The Nxc3x97N matrix can then be formed by adding an identity matrix I to the product of the Nxc3x97D basis set and the Dxc3x97N amplitude array.
Basis functions may comprise simple trigonometric functions that are well known and can be specified with a few parameters. Alternately, the basis functions may depend upon characteristics of the differences between the measured spectra values and the reference spectra values. Weightings of the basis functions may be stored in the color sensing device when the basis functions are known and fixed (e.g., when they are a set of simple trigonometric functions). When the basis functions are variable, both the basis functions and associated basis function weightings may be stored in the color sensing device (e.g., when the basis functions are principal components obtained from the measured data).
The known reference reflectance spectra values may be either calibration spectra values or simulation spectra values. The known reference reflectance spectra values may be obtained from a reference instrument.